Self-Adjoint Second-Order Equations for Fermions and the Foldy–Wouthuysen Representation

Abstract

Self-adjoint second-order equations with spinor wave functions in an external electromagnetic field are obtained for fermions. The relationship is found between these equations and the Dirac equations in the Foldy–Wouthuysen representation. Closed chiral symmetric equations are written for left and right spinors by using the Dirac matrices in chiral representation. A closed chiral symmetric Foldy–Wouthuysen equation is obtained for an arbitrary electromagnetic field. There are no summands mixing left and right spinors in these equations irrespective of the presence or absence of fermion mass.